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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > A diffusion limit for a model of interacting spins/queues with log-linear interaction

## A diffusion limit for a model of interacting spins/queues with log-linear interactionAdd to your list(s) Download to your calendar using vCal - Vadim Shcherbakov (Royal Holloway, University of London)
- Tuesday 06 August 2024, 15:30-16:00
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If you have a question about this talk, please contact nobody. SSDW02 - Stochastic reflection This talk concerns a diffusion limit for an interacting spin model defined in terms of a multi-component Markov chain whose components (spins) are indexed by vertices of a finite graph. The spins take values in a finite set of non-negative integers and evolve subject to a graph based log-linear interaction. We show that if the set of possible spin values expands to the set of all non-negative integers, then a time-scaled and normalised version of the Markov chain converges to a system of interacting Ornstein-Uhlenbeck processes reflected at the origin. This limit is akin to heavy traffic limits in queueing (and our model can be naturally interpreted as a queueing model). Our proof draws on developments in queueing theory and relies on martingale methods. Although the idea of the proof is similar to those used for obtaining heavy traffic limits, some modifications are required due to the presence of interaction. The talk is based on the joint work with Anatolii Puhal’skii. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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